I am so sorry for misleading you. I needed to solve this problem, because it occurred to me whilst I was solving another one. Indeed, what I had written is not true. In such case, could you help me find all integers for which

i divisible by

?

Sep 21st 2011, 11:18 AM

Opalg

Re: Divisibility

Quote:

Originally Posted by gollum

Could somebody help me prove that for any integer

i divisible by

?

I have already tried proving it using induction but I got stuck in the final step where n=k+1. Please, help.

Have you checked what happens if you try putting n=2, or n=3?

Sep 21st 2011, 11:25 AM

HallsofIvy

Re: Divisibility

It is impossible to prove something that is NOT true! What reason do you have to believe that this statement is true?

Sep 21st 2011, 12:25 PM

gollum

Re: Divisibility

Hi! I have already corrected the post.

Sep 21st 2011, 01:03 PM

Opalg

Re: Divisibility

You could try to show that the ratio increases towards a limiting value 4. The ratio is equal to 3 when n=1. For n>1, it will lie between 3 and 4, so can never again be an integer.

Sep 21st 2011, 01:33 PM

gollum

Re: Divisibility

Thanks, but how do I find maximum and minimum of a function like this - I mean it is exponential as well as rational.

Sep 22nd 2011, 12:40 AM

Opalg

Re: Divisibility

Probably the easiest approach is to write in the form . Then show that that fraction is positive and less than 1 when n>1.